Search each folder's log that has your character name on it. Then it contains your character's HUD :)
Copy the ADDON.DAT and HOTBAR.DAT to your alt's folder.
Source: Reddit.
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This thread might be taken down now. When people first started advertising this method on the official forums, all the threads disappeared almost overnight. SE has a hard stance against telling people to go into the game folders and mess with the DAT files directly instead of through the built-in backup.